Step-by-step explanation:

let g(x) = x-2

This emplies that x =2

given f(x) = 2x^3 - 3 x^2 - 17x +30

so, f(2) = 2(2)^3 - 3(2)^2 - 17(2) + 30

= 16 -12 -34 +30

=0

so x-2 is a factor of given polynomial

Verified answer

➡HERE IS YOUR ANSWER

Now,

f(x)

[tex]\begin{gathered}2 {x}^{3} - 3 {x}^{2} - 17x + 30 \\ \\ = 2 {x}^{3} - 4 {x}^{2} + {x}^{2} - 2x - 15x + 30\\ \\ =2 {x}^{2} (x - 2) + x(x - 2) - 15(x - 2) \\ \\ = (x - 2)(2 {x}^{2} + x - 15) \\ \\ = (x - 2)(2 {x}^{2} + 6x - 5x - 15) \\ \\ = (x - 2)(2x(x + 3) - 5(x + 3)) \\ \\ = (x - 2)(x + 3)(2x - 5)\end{gathered} [/tex]

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